Reduction formula for point group D8h
Your representation
E |
2C8 |
2(C8)3 |
2C4 |
C2 (z) |
4C2' |
4C2'' |
i |
2(S8)3 |
2S8 |
2S4 |
h |
4v |
4d |
72 |
0.0000 |
-0.0000 |
0 |
0 |
-4 |
-2 |
0 |
-0.0000 |
0.0000 |
0 |
24 |
4 |
2 |
can be reduced to
A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
E3g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
E3u |
3 |
3 |
3 |
3 |
3 |
6 |
3 |
0 |
3 |
1 |
2 |
6 |
3 |
6 |
Substraction of translational and rotational contributions results in
A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
E3g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
E3u |
3 |
2 |
3 |
3 |
2 |
6 |
3 |
0 |
2 |
1 |
2 |
5 |
3 |
6 |
Force field analysis
Infrared and Raman activities (harmonic approximation)
Method |
A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
E3g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
E3u |
Infrared |
- |
- |
- |
- |
- |
- |
- |
- |
+ |
- |
- |
+ |
- |
- |
Raman |
+ |
- |
- |
- |
+ |
+ |
- |
- |
- |
- |
- |
- |
- |
- |
No. 1 : Total number of force constants .
No. 2 : Total number of force constants k.
No. 3 : Total number of nonvanishing force constants k.
Symmetry properties of force field parameters
Force field |
A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
E3g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
E3u |
linear |
3 |
2 |
3 |
3 |
2 |
6 |
3 |
0 |
2 |
1 |
2 |
5 |
3 |
6 |
quadratic |
100 |
64 |
82 |
80 |
119 |
162 |
117 |
59 |
61 |
58 |
59 |
155 |
118 |
153 |
cubic |
1682 |
1646 |
1667 |
1665 |
2933 |
3331 |
2935 |
1435 |
1505 |
1454 |
1490 |
3321 |
2943 |
3323 |
quartic |
28141 |
27476 |
27842 |
27772 |
52523 |
55606 |
52521 |
26231 |
26301 |
26247 |
26283 |
55463 |
52530 |
55461 |
Number of independant internal coordinates |
3 |
Literature
- J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement